This invention relates generally to Free Space Optical (FSO) communications, and in particular to correction of tip-tilt aberrations in FSO signals.
FSO performance depends upon several factors, including the atmospheric seeing condition, weather, and the local environment. Atmospheric seeing is generally quantified by the length over which the phase of an optical wavefront in the propagation path has 1 radian RMS variance, as described by the Fried parameter, ro. Atmospheric seeing can also be expressed as an angle (e.g., in radians), determined by the mean beam divergence caused by the atmosphere.
Atmospheric seeing is a function of the atmospheric refractive index structure constant, Cn2 along the path of beam propagation. The effects of atmospheric seeing on an FSO signal presents an effective limiting aperture size of ro for an arriving wavefront, leading to degraded spatial resolution. For a telescope with a physical aperture diameter that is less than the effective limiting aperture size (D<ro), diffraction dominates. In cases where the telescope's physical aperture diameter is approximately equal to the effective limiting aperture size (D˜r0), first order Zernike polynomial (tip-tilt) aberrations dominate the aberration error in an FSO signal. When the telescope's physical aperture diameter is significantly larger than the effective limiting aperture size (D >>r0), the aberration error in an FSO signal is dominated by the effects of high order aberrations.
Consequently, there are three domains to consider. 1). Diffraction limited. When D<ro the effects of the telescope's physical aperture size dominate over the effects of atmospheric seeing. Thus, correcting for atmospheric seeing effects is of little to no value. 2). Good seeing conditions. This is generally defined as the ratio of the telescope's physical aperture diameter (D) and the effective limiting aperture size (ro) being greater than about 1 (i.e., not diffraction limited) and less than about 5. Under good seeing conditions, tip-tilt aberrations, corresponding to motion of the centroid of the FSO signal, are the major contributors to the aberration error. According to one analysis, for pure, well developed atmospheric turbulence, tip-tilt aberrations comprise 87% of the total aberration error. Thus, under good seeing conditions, compensation for tip-tilt type aberrations can provide a dramatic improvement in obtainable resolution. 3. Bad seeing conditions. This is generally defined as the ratio of the telescope's physical aperture diameter (D) and the effective limiting aperture size (ro) being greater than about 5. In bad seeing conditions, higher order aberration contribute significantly to the aberration error, and thus correcting for just the tip-tilt aberrations does not provide a significant improvement in obtainable resolution.